i don't have any data or anything, but yeah i'll stand by that.  even when a bite or penitence or somesuch seals the deal, it's usually an autoattack of some kind that actually score the kill.

i think the reason for this is that people know when they are getting near the critical-danger HP level where one ability can finish them and they try to break off before than. player B knows that player A knows that he's in danger, so player B uses the ability while he still can, before player A breaks off. this leaves player A with an extremely low amount of HP, rendering him killbait.

the principal exception to this is snipe.  Spit too, sometimes.

It's the burst damage that usually causes a person to run.  And if the pursuer is faster, then you are dead to autoattacks.  But if you were to look at the damage you receive before you ran, it is invariably burst damage or some type of damage that bypassed the armor which causes the majority of damage. It's not damage over the whole course of the battle that matters - it's the damage up to the point when someone decides to turn tail.  So even if you start to break even with armor at say 5K health, that is misleading if you start to run with 2K health left.

Not until the late game do autoattacks really come into their own.  So armor gains some significance when you start getting a few artifacts, but until then, HP just seems to rein supreme.  This is even moreso in large games where you may have 3 DGs that all drop their abilities on you at the outset.

Furthermore, there is the psychological effect.  If I have 4.5K hits and my opponent has 7K hits, I can tell you that I am less likely to go for a straight up 1v1.  It maybe that I have enough armor to overcome the HP difference, but I will not know that until it gets to a point where I will be unable to retreat if I do not.

Armor is a flat improvement. It doesn't look like it since the % reduction per point of armor decreases, but the percentage of effective HP you gain is linear. To demonstrate, imagine you have 25% damage reduction from your armor. If you have X hp, then when X flat damage hits you, you stil have .25X left. If armor didn't apply to this remaining hp, then you would have exponentially diminishing returns. But since it obviously does, you have to sum the infinite series (.25)^k for 1<k<infinity. This is a simple geometric series so you must take 1/(1-.25)-1 = .333x additional damage before you die. If you have 50% reduction, this is double the amount of damage reduction, but it gives you more than double the effective hp compared to 25% reduction. Same formula applies: 1/(1-.5)-1=1, so you must take x additional damage before you die. In this case you can take 3 times as much additional damage for 2 times the % reduction.

The reason comparing it to your current health is relevant is because your health increases throughout the game. Armor bonuses get better the more health you have, health bonuses do not. 1000 armor at level 20 provides more benefit than at the beginning. 1000 hp provides the same core benefit (aside from the fact that you have more armor at the end).

That's exactly right, and is the "real world" situation the theorycrafts ignore.  If you take a frontloaded 2k from nukes out of your 4000 hp, you are not going to stand and fight and rely on your amazing armor - you are going to run lest you eat more nukes or maybe a snipe from beyond.  If you are running you aren't dealing any autoattack damage to them, but they may be to you.

You might die to autoattacks but it's not what killed you.

No, armor helps vs auto attack only.

And minion damage, and Rook towers I believe.

No, that's wrong, and is the point I've been making all along.

Ability damage is unaffected by armor, so all hp and no armor does help greatly against it!  + 1000 hp/0 armor helps in so many more situations than +500 hp/+300 armor because you will die to that 600 dmg pounce now, where before you would have lived.

You are right that armor begins to matter more, but it is not at the 4K-5K range for the reasons I stated above.   You are going to flee well before you get close to zero damage so the better metric to use is the point at which you flee.  So even if you have 5K hits, if you are fleeing at 2K hits, then the better metric of your staying power is 3K, not 5K.  Using 3K as the metric, at least a third of that damage will be done at T=0 and possibly more in a 1v1 fight.  If you are involved in a 2v2 straight-up fight, at least 2/3 of your staying hitpoints will be done at T=0 if the damage is focused.  (And God help you if Reg is sitting off in the wings waiting to snipe).  You are way better off having 8K total HP (6K v. 3K staying HP) and no armor than you are with 5K HP and some large amount armor.

Late in the game when people get vasts amounts of AA increases and attack speed increases, armor makes a lot more sense.  But this is late in the game when people start stacking artifacts and at this point the game is typically decided.  There are always games that will be the exception, but I typically fear a UB coming at me with 8K hits more than a UB coming at me with 5K hits.  A big exception for me is a map with a couple of rooks or a lot of defensive towers.  That is when armor makes much more sense because it gives you more staying power when you are knocking down defensive structures.  Other than that, I stack HP until I start doubling up on artifacts.

This is pretty much it for UB, Sedna, Erebus, and Oak, but you can switch some things up.

Instead of the scalemail or gauntlets you can get unbreakable boots and hauberk (if you're a general) for more hp at the expense of armor and damage - which is better in the end for the reasons listed above.

err no heart of life in that item build. Not going to be able to tank more than 1 push...

I end up with over 50hp regen per second, and by the point i have those items I usually have 5+ kills anyway. I have never personally needed to use HoL ever, and rarely get beaten by people who have it because they will be dead before they get away to use it. Only time I ever have problems with HoL is with a shielding Oak, for obvious reasons...

I do sometimes buy a robust rejuv potion, depending on map and whether I buy vlemish around lvl 5 or not (roll + slam eats mana).

(edit: rooks shoulder weapons + wand of speed really f&$%'s up HoL users) 

Armor is good for decreasing incoming damage. *waits* 

And as Melric said, it's about how much you take until the "I better run" HP level.  You're going to be hit with a frontload of ability damage in battle, followed by autoattacks, followed by more ability damage as the cooldowns finish.  The priests immediately heal you after you take the frontload. (Assuming you were at full already)  The amount they heal will be based off your max hp, and the amount you get back will be extremely important towards keeping you above the "I better run" HP amount.

It's going to be ability damage that decides that for a majority of the game.